Integration by Substitution

Trying to integrate (arcsin(x))^2/(sqrt 1-x^2)
So far i have made
arcsin x = u and
du=1/(sqrt1-x^2).dx

I am at u^2 * du

I have spent hours on this and it appears obvious but i just don't get it! sorry
Any pointers i would be extremely grateful. I feel its something to do with the calculus relationship between the values of arcsin and du.
Thanks in advance
Ken

Trying to integrate (arcsin(x))^2/(sqrt 1-x^2)
So far i have made
arcsin x = u and
du=1/(sqrt1-x^2).dx

I am at u^2 * du

I have spent hours on this and it appears obvious but i just don't get it! sorry
Any pointers i would be extremely grateful. I feel its something to do with the calculus relationship between the values of arcsin and du.
Thanks in advance
Ken

you make the substitution , find , so the integral becomes:

.

Look OK to me.

Now:

which can be checked by differentiating it, you should get the integrand back.